where
\(d(t) = U_n^\dagger \ d \ U_n\)  is the dipole operator and
\(E_{\mathrm {in}}(t)\)  is the incoming-field operator.
Here,
\(d = \sum _i d_{ei} (\sigma _{i2}^\dagger + \mbox{H.c.})\) ,
\(E_{\mathrm {in}}(t) = \sum _\omega i\epsilon (a_\omega + b_\omega ) e^{-i \omega t} + \mbox{H.c.}\) , and
\(d_{ei} \epsilon = \hbar g\) .
Definition (REF ) is very close to our classical notion of work [1]}, [2]} (to see that, one can think of an initial coherent, or semiclassical, incoming pulse \(|\alpha \rangle \) , fulfilling \(a_\omega |\alpha \rangle  = \alpha _\omega |\alpha \rangle \) , as established by Glauber [3]}).
In the rotating-wave approximation, and using the initial global state
\(|a_n\rangle _1|b_n\rangle _2|1^b\rangle \) ,
we find that (see Methods)
\(\langle W_{\mathrm {in}} \rangle _{a_1,b_2}= \langle W_{\mathrm {abs}} \rangle _{a_1,b_2} + \langle W_{\mathrm {reac}} \rangle _{a_1,b_2},\) 
